The location of the find does make a big difference. It strikes me that the shape of the skull leading down onto the beak is quite straight where as on most ducks this is curved. I wonder if it may be a small goose, the snow goose has a skull only 8cm long which is the same as this skull, another possible line of enquiry?

Goldeneye also has a green head, lives in Canada and has a skull the same size as this skull. Many of the featrures are closer to a Goldeneye than a Mallard, but as I suggested in my first post I would lean towards an ornimental race of duck. I learn't a long time ago to photograph everything before I prepare the skull and despite this I still have skulls which I am uncertain of the correct identity.